Approximate k-Cover in Hypergraphs: Efficient Algorithms, and Applications
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Given a weighted hypergraph H(V, E⊆ 2^V, w), the approximate k-cover problem seeks for a size-k subset of V that has the maximum weighted coverage by sampling only a few hyperedges in E. The problem has emerged from several network analysis applications including viral marketing, centrality maximization, and landmark selection. Despite many efforts, even the best approaches require O(k n n) space complexities, thus, cannot scale to, nowadays, humongous networks without sacrificing formal guarantees. In this paper, we propose BCA, a family of algorithms for approximate k-cover that can find (1-1/e -ϵ)-approximation solutions within an O(ϵ^-2n n) space. That is a factor k reduction on space comparing to the state-of-the-art approaches with the same guarantee. We further make BCA more efficient and robust on real-world instances by introducing a novel adaptive sampling scheme, termed DTA.
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